After wisely walking away from the car crash of Marvel’s 2015 film Ant-Man, Shaun of the Dead director Edgar Wright is back in the fast lane with his most thrillingly cinematic romp. A romantic musical disguised as a car-chase thriller, Baby Driver combines the over-cranked action fantasies of Hot Fuzz with the poptastic sensibilities of Scott Pilgrim vs the World. At its centre is Ansel Elgort’s eponymous getaway driver, who uses earphones to drown out the “hum-in-the-drum” of tinnitus (the result of a childhood accident) and orchestrates his life to carefully chosen iPod playlists. Whether he’s burning rubber or fixing a peanut butter sandwich (“right up to the edges”), this former joyrider spins his wheels and records with the same infectious exuberance. Think An American in Paris meets The French Connection, or Walter Hill’s The Driver as remade by Baz Luhrmann – it really is that much of a blast.

Accidentally indebted to smooth criminal Doc (Kevin Spacey), Baby is always “one more job” away from freedom. At home he cares for foster father Joseph (CJ Jones), who listens to music with his fingertips, and from whom Baby has learned signing and lip-reading – invaluable skills. At work he’s surrounded by wild cards: Buddy and Darling (Jon Hamm and Eiza González), a latter-day Bonnie and Clyde with matching his and hers tattoos; Bats (Jamie Foxx), a loose cannon who claims the monopoly on “mental problems”; Jon Bernthal’s ever-gruff Griff; rocker Flea’s Eddie No-Nose (formerly Eddie the Nose – don’t ask); and Lanny Joon’s JD, who “puts the Asian in home invasion”.

Wright directs with the confidence of someone who can afford to pay fanboy homage to his antecedents

The only sure thing in Baby’s life is his growing love for waitress Debora (Lily James), who does indeed “look like a zebra” in her black and white diner uniform, and who sings “B-A-B-Y” to herself as she waits tables, dreaming of heading west “in a car I can’t afford, with a plan I don’t have”. The ghosts of Tony Scott’s True Romance and Jim McBride’s Breathless (and the movies that inspired those films) haunt their whirlwind romance, a pulp fiction mash-up of comic-strip tropes, fired by palpable human chemistry.

Anyone familiar with Wright’s 2003 music video for Mint Royale’s Blue Song, in which Noel Fielding danced in the seat of a parked getaway car, will know that the writer/director has been nurturing Baby Driver for years. Indeed, the film opens with an explicit nod to its small-screen dry run, with Elgort lip-synching to Bellbottoms (“fabulous, most groovy”) by the Jon Spencer Blues Explosion while his cohorts rob a bank. Later, he halts a job until he’s correctly cued up the frantic bass riff opening of the Damned’s Neat Neat Neat, and searches for Golden Earring’s Radar Love before flooring a jacked ’86 purple Chevy Caprice. As for that “one killer track”, Queen fetishist Wright brilliantly turns to Brighton Rock to provide battling guitar accompaniment to a multistorey showdown of head-banging elegance.

It’s not just the action sequences that strike a chord. The toe-tapping opening titles find Baby doing an on-foot coffee run to the beats of Bob & Earl’s Harlem Shuffle, lyrics magically appearing on walls and signs in a scene as seamless as the opening freeway dance from La La Land. At times the songs serve as an on-the-nose Greek chorus, telling us that Baby has “nowhere to run to, nowhere to hide” as he’s trapped in an arms deal. But it’s when the horns and drums of the Button Down Brass’s Tequila become gunfire, or the madness of Hocus Pocus by Focus drives a breathless chase, that Wright really puts his foot down, with exhilarating results.

On the set of Edgar Wright’s Baby Driver: ‘Everything is fun with Jamie Foxx around’

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“You’re either hard as nails or scared as shit,” Baby is told, although like the young bucks of Ferris Bueller’s Day Off or Risky Business, he’s actually a bit of both. As for Wright, he directs with the confidence of someone who can afford to pay fanboy homage to his antecedents, whether casting Paul Williams as the Butcher in a nod to Smokey and the Bandit, or getting Kevin Spacey to bark “Don’t feed me any more lines from Monsters Inc… it pisses me off!”

A top-flight stunt co-ordination team (Darrin Prescott, Robert Nagle, Jeremy Fry) and a hip choreographer (Ryan Heffington) work together in perfect harmony, while cinematographer Bill Pope uses the Atlanta locations with the same affection that John Landis brought to Chicago in The Blues Brothers. If you want a soporific night out, go see Hampstead. For something with a little more torque, then, Baby, it’s you.

• Mark Kermode will deliver this year’s Philip French memorial lecture on Tuesday 18 July as part of Cinema Rediscovered at the Bristol Festival of Ideas. Click here for details